Abstract

Compactifying N = (1, 0) theories on a torus, with additional fluxes for global symmetries, we obtain N = 1 supersymmetric theories in four dimensions. It is shown that for many choices of flux these models are toric quiver gauge theories with singlet fields. Particularly we compare the anomalies deduced from the description of the six dimensional theory and the anomalies of the quiver gauge theories. Also, we give predictions for anomalies of four-dimensional theories corresponding to general compactifi cations of M5-branes probing C 2/Z k singularities.

Here, we study the T 2 compactification of a class of 6dmore » $$ \mathcal{N}=\left(1,\;0\right) $$ theories that is Higgsable to $$ \mathcal{N}=\left(2,\;0\right) $$ theories. We show that the resulting 4d N=2 theory at the origin of the Coulomb branch and the parameter space is generically given by two superconformal matter sectors coupled by an infrared-free gauge multiplet and another conformal gauge multiplet. Our analysis utilizes the 5d theories obtained by putting the same class of 6d theories on S 1. Our class includes, among others, the 6d theories describing multiple M 5 branes on an ALE singularity, and we analyze them in detail. The resulting 4d theory has manifestly both the SL(2,Z) and the full flavor symmetry. We also discuss in detail the special cases of 6d theories where the infrared-free gauge multiplet is absent. In an appendix, we give a field-theoretical argument for an F-theoretic constraint that forbids a particular 6d anomaly-free matter content, as an application of our analysis.« less

Here, we discuss reductions of generalmore » $$ \mathcal{N}=1 $$ four dimensional gauge theories on $$ {\mathbb{S}}^2 $$. The effective two dimensional theory one obtains depends on the details of the coupling of the theory to background fields, which can be translated to a choice of R-symmetry. We argue that, for special choices of R-symmetry, the resulting two dimensional theory has a natural interpretation as an $$ \mathcal{N}(0,2) $$ gauge theory. As an application of our general observations, we discuss reductions of $$ \mathcal{N}=1 $$ and $$ \mathcal{N}=2 $$ dualities and argue that they imply certain two dimensional dualities.« less

We discuss two infinite classes of 4d supersymmetric theories, T N(m) and Umore » $$(m)\atop{N}$$, labelled by an arbitrary non-negative integer, m. The T N(m) theory arises from the 6d, A N-1 type N=(2,0) theory reduced on a 3-punctured sphere, with normal bundle given by line bundles of degree (m + 1, -m); the m = 0 case is the N=2 supersymmetric T N theory. The novelty is the negative-degree line bundle. The U$$(m)\atop{N}$$ theories likewise arise from the 6d N=(2,0) theory on a 4-punctured sphere, and can be regarded as gluing together two (partially Higgsed) T N(m) theories. The T N(m) and U$$(m)\atop{N}$$ theories can be represented, in various duality frames, as quiver gauge theories, built from T N components via gauging and nilpotent Higgsing. We analyze the RG flow of the U($$(m)\atop{N}$$ theories, and find that, for all integer m > 0, they end up at the same IR SCFT as SU(N) SQCD with 2N flavors and quartic superpotential. The U$$(m)\atop{N}$$ theories can thus be regarded as an infinite set of UV completions, dual to SQCD with N f = 2N c. The U$$(m)\atop{N}$$ duals have different duality frame quiver representations, with 2m + 1 gauge nodes.« less

Here, we study certainmore » $$ \mathcal{N}=1 $$ preserving deformations of four-dimensional $$ \mathcal{N}=2 $$ superconformal field theories (SCFTs) with non-abelian flavor symmetry. The deformation is described by adding an $$ \mathcal{N}=1 $$ chiral multiplet transforming in the adjoint representation of the flavor symmetry with a superpotential coupling, and giving a nilpotent vacuum expectation value to the chiral multiplet which breaks the flavor symmetry. This triggers a renormalization group flow to an infrared SCFT. Remarkably, we find classes of theories flow to enhanced $$ \mathcal{N}=2 $$ supersymmetric fixed points in the infrared under the deformation. They include generalized Argyres-Douglas theories and rank-one SCFTs with non-abelian flavor symmetries. Most notably, we find renormalization group flows from the deformed conformal SQCDs to the ( A1,An) Argyres-Douglas theories. From these "Lagrangian descriptions," we compute the full superconformal indices of the ( A1,An) theories and find agreements with the previous results. Furthermore, we study the cases, including the TN and R0,N theories of class S and some of rank-one SCFTs, where the deformation gives genuine $$ \mathcal{N}=1 $$ fixed points.« less

We study certain N=1 preserving deformations of four-dimensional N=2 superconformal field theories (SCFTs) with non-abelian flavor symmetry. The deformation is described by adding an N=1 chiral multiplet transforming in the adjoint representation of the flavor symmetry with a superpotential coupling, and giving a nilpotent vacuum expectation value to the chiral multiplet which breaks the flavor symmetry. This triggers a renormalization group flow to an infrared SCFT. Remarkably, we find classes of theories flow to enhanced N=2 supersymmetric fixed points in the infrared under the deformation. They include generalized Argyres-Douglas theories and rank-one SCFTs with non-abelian flavor symmetries. Most notably, wemore » find renormalization group flows from the deformed conformal SQCDs to the (A1, An) Argyres-Douglas theories. From these “Lagrangian descriptions,” we compute the full superconformal indices of the (A1, An) theories and find agreements with the previous results. Furthermore, we study the cases, including the TN and R0,N theories of class S and some of rank-one SCFTs, where the deformation gives genuine N=1 fixed points.« less